Finite Group DatabasebetaFinite Group Databasebeta| order | 512 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #10586404 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C219 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C22 | C27 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
35906 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32 |
Polycyclic presentation:
2^9|b^a=bh,c^a=ci,d^a=dh,g^a=gi,c^b=ch,f^b=fi,e^c=ei140 conjugacy classes — view the full character table.
| maximal subgroup of | #72224136, #72225694, #72225712, … |
| maximal normal subgroup of | #72224136, #72225694, #72225712, … |
| maximal quotient of | #72219280, #72219286, #72232067, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(512, 10493600);